Find the Domain and Range x=y^13

$x = y^{13}$

Step 1

Rewrite the equation as $y^{13} = x$ .

$y^{13} = x$

Step 2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$y = \sqrt[13]{x}$

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 4

The range is the set of all valid $y$ values. Use the graph to find the range.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${y | y \in ℝ}$

Step 5

Determine the domain and range.

Domain: $(- \infty, \infty), {x | x \in ℝ}$

Range: $(- \infty, \infty), {y | y \in ℝ}$

Step 6

Find the Domain and Range x=y^13

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